From: "Seth Russell" <seth@robustai.net>
Subject: Re: Layering LX (or FOL) on RDF
Date: Tue, 27 Aug 2002 11:15:43 -0700
> From: "Peter F. Patel-Schneider" <pfps@research.bell-labs.com>
>
> > From: "Seth Russell" <seth@robustai.net>
> >
> > > From: "Peter F. Patel-Schneider" <pfps@research.bell-labs.com>
[...]
> > However, suppose you have a way of representing formulae in RDF. This will
> > have to use resources and statements. When you represention ~p, you will
> > have to have an RDF graph with a resource for the formula p and another resource
> > for the formula ~p. How can you allow this, and forbid the RDF graph that
> > is your RDF graph for ~p except that it replaces the resource for p with
> > the resource for ~p?
>
> I don't understand your paragraph. p is not a formula ... can never be a
> formula, in my view. Doesn't "p" just identify a node or represent a
> resource? {p negation ~p} is a formula.
I don't understand how p cannot be a formula. Primitive propositions are
formulae, and they seem to be naturally represented by resources.
What is { p negation ~p }? Is it a set?
I would represent negation,
> conjunction, and disjuntion formula as per this mentograph:
>
> http://robustai.net/mentography/negation_conjunction_disjunction.gif
What is the connection between this and RDF? I don't see any, and the
point of this discussion is representing logic in RDF.
> What is the problem again with these kind of arrows ?
Well, lots, including the fact that the arrows are not RDF statements, as
they are more than triples.
> <snipping stuff who's complexity I do not understand>
>
> > Truth and falsity are represented by inclusion in the classes pl:Truth and
> > pl:Falsity, respectively.
>
> Ok, the pink resources (which are formula) can be of of rdf:type pl:Truth or
> pl:Falsity relative to some other graph.
>
> > To forbid self-reference, you have to *forbid* RDF graphs that contain
> > things like
> > _:x pl:negation _:x .
>
> I have no problem with calling that formula rdf:type pl:Falsity relative to
> any graph that purports to be binarilay logical. But I dont' know if we
> must forbid it, I mean anybody can say anything about anything ... can't
> they?
Well the problem is that if you make this formula belong to pl:Falsity,
then the rules of logic say that it must belong to pl:Truth, and the rules
of logic also say that pl:Truth and pl:Falsity are disjoint. Similarly, if
you make it belong to pl:Truth, then the rules of logic say that it must
belong to pl:Falsity. So no matter what you do, you get into a bind.
> Seth Russell
> http://robustai.net/sailor/
peter